Place your oven rack in the center position and preheat the oven to 400 degrees. Prepare two 12 cup muffin pans with paper liners or wiping with a thin coating of oil.
In a medium mixing bowl: use a fork to combine dry ingredients – flour, baking powder, baking soda, and salt.
In a large mixing bowl (or the bowl of a stand mixer): beat eggs and sugar on low/medium speed until they become light in color and double in volume. Continue mixing on low speed while adding the yogurt, milk and oil.
Gently mix in the dry ingredients adding ⅓ of mixture at a time. Mix just enough for incorporate the dry into the liquid. Use a wooden spoon or silicon spatula, and light hand, to fold the blackberries into the muffin batter. Fold the batter over 3 -5 times, just enough to distribute the fruit throughout the batter - without dying the entire mixture purple.
In a small bowl, combine the brown sugar, flour, and cinnamon for the topping. Use a fork or your fingers to work the butter into the mixture until it becomes the texture of wet sand.
Portion the batter into the prepared muffin cups so they are approximately ⅔ full - a scant ¼ cup of batter. Sprinkle the streusel mixture over the muffin tops.
Place the pans into the preheated oven to bake 17-20 minutes until a toothpick inserted into the center of a muffin comes out clean. Let the muffins cool completely before serving. Store any leftover muffins in an airtight container.